Porous body, honeycomb filter, and method for producing porous body

ABSTRACT

A porous body has a flow-rate-weighted mean diameter Ru of 10 μl or more and 24 μm or less, which is obtained as follows: with reference to porous-body data obtained by a CT scan in which positional information is associated with voxel-type information, a plurality of virtual curved surface solids, which are each a curved surface solid made up of a plurality of virtual spheres, are placed to fill space voxels (Step S 100 ); fluid analysis is carried out to obtain information regarding the flow rates of a fluid in individual space voxels during passing of the fluid through the porous body (Step S 110 ); and, the flow-rate-weighted mean diameter Ru is obtained, which is a weighted mean obtained by weighting the equivalent diameter R′ i  of each virtual curved surface solid with the volume V i  and average flow rate U i  of each virtual curved surface solid (Step S 120 ).

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a porous body, a honeycomb filter, anda method for producing a porous body.

2. Description of the Related Art

It is known that porous bodies are employed in exhaust-gas cleaningstructures such as honeycomb filters. For example, Patent Literature 1describes a method for producing a porous body in which a base materialcomposed of an inorganic material and a pore-forming agent are mixed toprovide green body; the green body is shaped into a compact; and thecompact is fired at a predetermined firing temperature. According tothis method for producing a porous body, a porous body having a hightrapping capability can be produced by setting the base material and thepore-forming agent so as to satisfy a predetermined range of(D90-D10)/D50 where D10 represents the particle size at 10 vol %, D50represents the particle size at 50 vol %, and D90 represents theparticle size at 90 vol %.

CITATION LIST Patent Literature

[PTL 1] International Publication No. 2013/146499

SUMMARY OF INVENTION

The higher capability of trapping particulate matter (PM) in exhaust gasporous bodies have, the more preferable they are. Thus, there has been ademand for a porous body having a higher trapping capability.

The present invention has been made in order to meet such a demand. Amain object of the present invention is to provide a porous body and ahoneycomb filter that have a higher trapping capability.

A porous body of the present invention has a flow-rate-weighted meandiameter Ru of 10 μm or more and 24 μm or less, wherein theflow-rate-weighted mean diameter Ru is obtained as follows:

based on an image obtained by three-dimensionally scanning the porousbody, porous body data is created in which positional informationindicating position of a voxel in the image is associated withvoxel-type information indicating whether the voxel is space voxelrepresenting space or matter voxel representing object;

a process is carried out in which a single parent virtual sphere isplaced in the porous-body data so as to have as large a diameter aspossible so that the parent virtual sphere fills space voxels withoutoverlapping the matter voxel, at least one child virtual sphere whosecenter overlaps the parent virtual sphere that has been placed is placedsuch that voxels occupied by the at least one child virtual sphere donot overlap the matter voxel and fill space voxels, and a single virtualcurved surface solid made up of the parent virtual sphere and the atleast one child virtual sphere is placed such that curved surface solidvoxels, which are voxels occupied by the virtual curved surface solid,fill space voxels; this process is repeated to place a plurality of thevirtual curved surface solids such that voxels occupied by differentvirtual curved surface solids do not overlap each other;

based on the porous-body data, fluid analysis is carried out by thelattice Boltzmann method in terms of a fluid flowing through apredetermined inflow plane into the porous body, to obtain flow-ratevectors of the fluid in individual space voxels during passing of thefluid through the porous body; and

based on information regarding the virtual curved surface solids thathave been placed and information regarding the flow-rate vectors inindividual space voxels, the flow-rate-weighted mean diameter Ru isobtained by an expression (1) below

$\begin{matrix}{\left\lbrack {{Math}.\mspace{14mu} 1} \right\rbrack \mspace{641mu}} & \; \\{{Ru} = \frac{\sum\limits_{i = 1}^{n}\left( {R_{i}^{\prime} \times V_{i} \times U_{i}} \right)}{\sum\limits_{i = 1}^{n}\left( {V_{i} \times U_{i}} \right)}} & (1)\end{matrix}$

where

Ru: flow-rate-weighted mean diameter [μm]

n: number of virtual curved surface solids that have been placed[number]

R′_(i): equivalent diameter of each virtual curved surface solid [μm](i=1, 2, . . . , n)

V_(i): volume of each virtual curved surface solid [cc] (i=1, 2, . . . ,n)

U_(i): average flow rate of fluid passing through each virtual curvedsurface solid [mm/s] (i=1, 2, . . . , n).

The inventors of the present invention have found that a filterincluding a porous body having a flow-rate-weighted mean diameter thatis not excessively large or small tends to have a high trappingcapability. The inventors have found that a flow-rate-weighted meandiameter Ru of 10 μm or more and 24 μm or less results in a sufficientlyhigh trapping capability. A porous body according to the presentinvention satisfies this condition and hence achieves a sufficientlyhigh trapping capability. This is probably achieved for the followingreason. The larger the extent of variation in volume or average flowrate among a plurality of virtual curved surface solids that have beenplaced, the larger the tendency for the flow-rate-weighted mean diameterRu to become excessively large or small. Regarding pores of a porousbody that are simulated with virtual curved surface solids having alarge volume, the probability that a fluid passing through the porescomes into contact with the wall surfaces of the porous body tends todecrease. Regarding pores of a porous body that are simulated withvirtual curved surface solids having a small volume, a fluid tends notto pass through the pores or a catalyst tends not to be appropriatelyapplied to the wall surfaces of the pores, the catalyst being used forthe porous body to be used as a filter. Regarding pores of a porous bodythat are simulated with virtual curved surface solids having an averageflow rate higher than the average flow rate (simple average flow rate)of the whole pores of the porous body, a fluid passes through thesepores in a short time and hence these pores tend not to contribute tothe trapping capability. Regarding pores of a porous body that aresimulated with virtual curved surface solids having an average flow ratelower than the average flow rate (simple average flow rate) of the wholepores of the porous body, the amount of a fluid entering these pores issmall and hence these pores tend not to contribute to the trappingcapability. As has been described, pores of a porous body that aresimulated with virtual curved surface solids having an excessively largeor small volume or an excessively high or low average flow rate tend notto contribute to the trapping capability. This is probably the reasonwhy, in porous bodies having a large portion that tends not tocontribute to the trapping capability, the flow-rate-weighted meandiameter Ru is found to be excessively large or small; and aflow-rate-weighted mean diameter Ru of 10 μm or more and 24 μm or lessresults in a sufficiently high trapping capability.

In such a case where a plurality of child virtual spheres are placed forplacing a single virtual curved surface solid, the plurality of childvirtual spheres are allowed to overlap each other. The fluid analysis iscarried out in terms of a fluid flowing from a predetermined inflowplane to a predetermined outflow plane of the porous body.

In a porous body according to the present invention, based on theinformation regarding the virtual curved surface solids that have beenplaced, an arithmetic mean diameter Rc=(R′₁+R′₂+ . . . +R′_(n))/n isobtained, and a difference ΔR (=|Ru−Rc|) is preferably 2 μm or less.When the difference ΔR satisfies this range, a higher trappingcapability tends to be achieved.

A honeycomb filter according to the present invention includes

a partition that include the porous body according to any one of theabove-described embodiments of the present invention and form aplurality of cells of which one end is open and the other end is sealedand serving as a fluid channel.

In this honeycomb filter, since the porous body forming the partitionssatisfies, for example, the above-described range of theflow-rate-weighted mean diameter Ru, a sufficiently high trappingcapability is achieved during passing of a fluid through the honeycombfilter.

A method for producing a porous body of the present invention includes:

a raw-material mixing step of mixing talc having an average particlesize of 1 μm or more and 18 μm or less, alumina, an auxiliary rawmaterial containing a material that undergoes a eutectic reaction withtalc and being prepared in an amount so as to satisfy a weight ratio of0.5% or more and 1.5% or less by weight relative to the talc, and apore-forming agent, to provide green body; and

a molding and firing step of molding the green body to provide a compactand firing this compact at a firing temperature of 1350° C. to 1440° C.

The inventors of the present invention have found that production of aporous body by the above-described production method including the stepsprovides a porous body having a higher trapping capability. The reasonfor this is probably as follows. Use of talc having an average particlesize of 18 μm or less probably results in suppression of generation ofexcessively large pores. By adding an auxiliary raw material containinga material that undergoes a eutectic reaction with talc, excessivelysmall pores through which a fluid tends not to pass are probably filled.In addition, the firing temperature of 1350° C. to 1440° C. probablyresults in a sufficiently high strength of the porous body. As a result,generation of excessively large or small pores is suppressed andgeneration of pores causing an excessively high or low flow rate issuppressed; and this probably results in a high trapping capability.Note that the production method allows production of the above-describedporous body according to the present invention, which has aflow-rate-weighted mean diameter Ru of 10 μm or more and 24 μm or less.

In a method for producing a porous body according to the presentinvention, the talc may have an average particle size of 5 μm or moreand 12 μm or less. The talc having an average particle size of 12 μm orless suppresses more effectively the above-described generation ofexcessively large pores.

In a method for producing a porous body according to the presentinvention, the weight ratio of the auxiliary raw material relative tothe talc is preferably 0.5% or more and 1.0% or less by weight. Theauxiliary raw material may be at least one selected from zirconiumoxide, cerium oxide, and yttrium oxide. In addition, the firingtemperature is preferably 1410° C. to 1430° C.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a front view of a honeycomb filter 30 including porouspartitions 44.

FIG. 2 is a sectional view taken along line A-A in FIG. 1.

FIG. 3 illustrates the configuration of a user personal computer 20serving as a microstructure analyzer.

FIGS. 4A and 4B illustrate conceptual views of porous-body data 60.

FIG. 5 is an explanatory view of porous-body data 60.

FIG. 6 is a flow chart illustrating an example of an analysis processingroutine.

FIG. 7 is a flow chart illustrating an example of anvirtual-curved-surface-solid placement process.

FIG. 8 is an explanatory view illustrating an example of anvirtual-curved-surface-solid table 83.

FIGS. 9A and 9B illustrate explanatory views of placement of a parentvirtual sphere.

FIGS. 10A and 10B illustrates explanatory views of placement of childvirtual spheres and a virtual curved surface solid.

FIG. 11 is a graph illustrating the relationship betweenflow-rate-weighted mean diameter Ru and the number of leaked particlesin Experimental examples 1 to 4.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, embodiments for carrying out the present invention will bedescribed with reference to the drawings.

FIG. 1 is a front view of a honeycomb filter 30 including porouspartitions 44 formed of a porous body according to an embodiment of thepresent invention. FIG. 2 is a sectional view taken along line A-A inFIG. 1. The honeycomb filter 30 is a diesel particulate filter (DPF)having a function of filtering off particulate matter (PM) in exhaustgas emitted from a diesel engine. The honeycomb filter 30 includes alarge number of cells 34 (refer to FIG. 2) defined by the porouspartitions 44. A peripheral protective part 32 is formed around thecells 34. The material of the porous partitions 44 is preferably aceramic material formed of inorganic particles of Si—SiC, cordierite, orthe like from the standpoint of strength and heat resistance. The porouspartitions 44 preferably have a thickness of 200 μm or more and lessthan 600 μm. This thickness is 300 μm in this embodiment. The porouspartitions 44 have an average pore size (measured by mercuryporosimetry) of 10 μm or more and less than 60 μm and a porosity (voidratio) of 40% or more and less than 65%, for example. As illustrated inFIG. 2, a large number of cells 34 formed in the honeycomb filter 30 aredivided into open-inlet cells 36 having an open inlet 36 a and an outlet36 b sealed with an outlet sealing material 38, and open-outlet cells 40having an inlet 40 a sealed with an inlet sealing material 42 and anopen outlet 40 b. Such open-inlet cells 36 and open-outlet cells 40 arealternately disposed so as to be adjacent to one another. The density ofthe cells is 15 cells/cm² or more and less than 65 cells/cm², forexample. The peripheral protective part 32 is a layer for protecting theperiphery of the honeycomb filter 30. The peripheral protective part 32may contain, for example, the above-described inorganic particles,inorganic fibers of aluminosilicate, alumina, silica, zirconia, ceria,mullite, or the like, and a binder such as colloidal silica or clay.

The honeycomb filter 30 is placed downstream of a diesel engine (notshown) and used to clean PM-containing exhaust gas to be released intothe air, for example. Arrows in FIG. 2 indicate flows of exhaust gas inthis occasion. The exhaust gas containing PM emitted from the dieselengine flows through the inlets 36 a of the honeycomb filter 30 into theopen-inlet cells 36, then passes through the porous partitions 44 intothe adjacent open-outlet cells 40, and is released through the outlets40 b of the open-outlet cells 40 into the air. While the exhaust gascontaining PM flows from the open-inlet cells 36 through the porouspartitions 44 into the open-outlet cells 40, PM is trapped; and hencethe exhaust gas having flowed into the open-outlet cells 40 is a cleanexhaust gas not containing PM. The interior of the pores of the porouspartitions 44 is coated with an oxidation catalyst such as platinum (notshown). The oxidation catalyst oxidizes trapped PM to thereby suppress adecrease in the porosity of the porous partitions 44 or a sharp increasein pressure loss.

The porous partitions 44 of this embodiment subjected to an analysis(described below) of the microstructure of the porous body forming theporous partitions 44, are found to have a flow-rate-weighted meandiameter Ru of 10 μm or more and 24 μm or less. It is more preferablethat a difference ΔR is 2 μm or less. Hereinafter, the method ofanalyzing the microstructure will be described.

FIG. 3 schematically illustrates the configuration of a user personalcomputer (PC) 20 designed as a microstructure analyzer for analyzing themicrostructure of the porous partitions 44. The user PC 20 includes acontroller 21 that includes, for example, a CPU 22 that executes variousprocesses, a ROM 23 that stores various processing programs or the like,and a RAM 24 that temporarily stores data; a HDD 25 that is a massstorage memory storing various processing programs such as analysisprocessing programs and various data such as porous-body data 60 that isthree-dimensional voxel data of a porous body. The user PC 20 isequipped with a display 26 that displays various information on thescreen and input devices 27 with which the user input various commands,such as a keyboard. As will be described in detail below, theporous-body data 60 stored in the HDD 25 includes a porous-body table 71and an inflow-outflow table 72. The user PC 20 functions to analyze themicrostructure of a porous body on the basis of the porous-body data 60stored in the HDD 25. During this analysis of the microstructure,porous-body data 80 is stored in the RAM 24. As will be described indetail below, the porous-body data 80 includes a porous-body table 81,an inflow-outflow table 82, and a virtual-curved-surface solid-table 83.

The HDD 25 of the user PC 20 stores, as the porous-body data 60, thethree-dimensional voxel data of the porous partitions 44 obtained bysubjecting the honeycomb filter 30 to a CT scan. In this embodiment, anXY plane defined by the X direction and the Y direction illustrated inFIG. 2 is selected as an imaging section; and a plurality of suchimaging sections are produced in the Z direction illustrated in FIG. 1.In this way, the CT scan is carried out to obtain voxel data. In thisembodiment, the resolution in each of the X, Y, and Z directions is 1.2μm, which provides a cube having 1.2 μm sides and serving as the minimumunit of three-dimensional voxel data, that is, a voxel. The resolutionin each of the X, Y, and Z directions can be appropriately set inaccordance with, for example, the performance of the CT scanner or thesize of particles to be analyzed. The resolutions in the directions maybe set to be different from each other. The resolutions in the X, Y, andZ directions may be, but not limited to, set to values within a range of0.5 to 3.0 μm, for example. Each voxel is identified in terms of itsposition by X, Y, and Z coordinates (a coordinate value of 1 correspondsto a length of a side of a voxel, 1.2 μm). The coordinates areassociated with type information indicating whether the voxel representsa space (pore) or an object (material of the porous partitions 44) andstored in the HDD 25. In this embodiment, voxels representing spaces(space voxels) are tagged with a type-information value of 0; and voxelsrepresenting objects (matter voxels) are tagged with a type-informationvalue of 9. Actually, the data obtained by a CT scan is luminance dataat individual X, Y, and Z coordinates, for example. The porous-body data60 used in this embodiment can be obtained by converting this luminancedata into a binary representation with respect to a predeterminedthreshold so that voxels are determined as to whether each voxel atcoordinates is a space voxel or a matter voxel. The predeterminedthreshold is set as a value that allows appropriate determination as towhether the voxels are space voxels or matter voxels. This threshold maybe empirically set in advance such that the measured porosity of theporous partitions 44 is substantially equal to the porosity of thebinarized voxel data, for example. Such CT scans can be carried out withSMX-160CT-SV3 manufactured by SHIMADZU CORPORATION, for example.

FIGS. 4A and 4B illustrate conceptual views of the porous-body data 60.FIG. 4A is a conceptual view of the porous-body data 60 obtained asvoxel data by subjecting, to a CT scan, the porous partition 44 in aregion 50 in FIG. 2. This porous-body data 60 in this embodiment isextracted from the voxel data of the porous partition 44. Theporous-body data 60 is voxel data of a rectangular parallelepipedportion having a length of 300 μm (=1.2 μm×250 voxels) in the Xdirection, which is the same as the thickness of the porous partition 44in the passing direction of exhaust gas, having a length of 480 μm (=1.2μm×400 voxels) in the Y direction, and having a length of 480 μm (=1.2μm×400 voxels) in the Z direction. This porous-body data 60 is subjectedto the analysis processing described below. Note that the dimensions ofthe porous-body data 60 can be appropriately set in accordance with, forexample, the thickness or size of the porous partition 44 or anacceptable calculation load. For example, the length in the X directionis not limited to 300 μm and may be another value that is the same asthe thickness of the porous partition 44 in the passing direction ofexhaust gas. The length in the X direction is preferably the same valueas the thickness of the porous partition 44 in the passing direction ofexhaust gas; however, the length and the thickness may be differentvalues. The lengths in the Y and Z directions are also not limited to480 μm and may be other values. The lengths in the Y and Z directionsmay be different from each other. Among the six planes of therectangular parallelepiped of the porous-body data 60, two planes(planes parallel to the Y-Z plane) are an inflow plane 61 (refer to FIG.2) that is a boundary surface between the porous partition 44 and theopen-inlet cell 36, and an outflow plane 62 (refer to FIG. 2) that is aboundary surface between the porous partition 44 and the open-outletcell 40 in the region 50; and the other four planes are sections of theporous partition 44. FIG. 4B illustrates an XY plane (imaging section)63 at a position where the Z coordinate is 3 in the porous-body data 60and an enlarged view 64 of a portion of the XY plane 63. As illustratedin the enlarged view 64, the XY plane 63 is made up of arranged voxelshaving 1.2 μm sides. Each voxel is expressed as a space voxel or amatter voxel. Note that the imaging section obtained by a CT scan is aplanar data having no thickness in the Z direction as illustrated inFIG. 4B. However, each imaging section is handled as having a thicknessof the gap (1.2 μm) between imaging sections in the Z direction. Inother words, each voxel is handled as a cube having 1.2 μm sides asdescribed above. Note that, as illustrated in FIG. 5, the porous-bodydata 60 is stored, in the HDD 25, as data including the porous-bodytable 71 in which the XYZ coordinates of each voxel serving aspositional information are associated with type information, and theinflow-outflow table 72 indicating the inflow plane 61 and the outflowplane 62. In FIG. 5, “X=1” in the inflow-outflow table 72 denotes theplane at X=1 of the XYZ coordinate system, that is, the inflow plane 61illustrated in FIG. 4A. Similarly, “X=251” denotes the outflow plane 62.The HDD 25 stores, in addition to the porous-body data 60, a pluralitypieces of other porous-body data representing the voxel data of theporous partitions 44 in terms of regions other than the region 50.

Hereinafter, analysis processing carried out by the user PC 20 for theporous-body data 60 will be described. FIG. 6 is a flow chart of ananalysis processing routine. This analysis processing routine is carriedout as follows: according to a command of carrying out analysisprocessing input by the user via the input devices 27, the CPU 22executes the analysis processing programs stored in the HDD 25.Hereinafter, the case of carrying out analysis processing of theporous-body data 60 will be described; however, analysis processing ofother porous-body data can be similarly carried out. The porous-bodydata that is to be analyzed may be set in advance or may be selected bythe user.

Upon start of the analysis processing routine, the CPU 22 executes anvirtual-curved-surface-solid placement process (Step S100) of placingvirtual curved surface solids so as to fill space voxels of theporous-body data 60.

Here, the description of the analysis processing routine is interruptedand the virtual-curved-surface-solid placement process will bedescribed. FIG. 7 is a flow chart of the virtual-curved-surface-solidplacement process. This virtual-curved-surface-solid placement processis executed by the CPU 22. Upon execution of the virtual-curved-surfacesolid placement process, the CPU 22 reads the porous-body data 60 storedin the HDD 25 and stores it in the RAM 24 (Step S200). As a result, thedata the same as the porous-body data 60 including the porous-body table71 and the inflow-outflow table 72 and stored in the HDD 25 is stored inthe RAM 24 as the porous-body data 80 including a porous-body table 81and an inflow-outflow table 82. In the porous-body data 80 that havebeen read, virtual wall surfaces are defined (Step S210). Specifically,the user inputs via the input devices 27 the distance from theporous-body data 80 that is a 300 μm×480 μm×480 μm rectangularparallelepiped to the surrounding virtual wall surfaces; and the CPU 22receives this input and stores it in the RAM 24. For example, in a casewhere the distance to the virtual wall surfaces is defined as 1 μm, theCPU 22 recognizes that the virtual wall surfaces are present 1 μmoutside the planes of the porous-body data 80 in the X, Y, and Zdirections, and that regions outside the virtual wall surfaces are fullyoccupied by matter voxels. Specifically, since the porous-body data 80is a 300 μm×480 μm×480 μm rectangular parallelepiped, it is recognizedas being covered by the virtual wall surfaces that form a 302 μm×482μm×482 μm rectangular parallelepiped. These virtual wall surfaces areset in order to define the region within which virtual curved surfacesolids (parent virtual spheres and child virtual spheres) describedbelow can be placed.

Subsequently, the CPU 22 sets the diameter Ra of a parent virtual sphereto a maximum value Ramax (Step S220) and determines as to whether or notthe parent virtual sphere having the diameter Ra can be placed withinspace voxels inside the virtual wall surfaces defined in Step S210 (StepS230). The parent virtual sphere having the diameter Ra is a virtualsphere that has a size with a diameter of Ra (μm) and whose center ispositioned at the center of one of voxels. Whether or not the parentvirtual sphere having the diameter Ra can be placed is determined in thefollowing manner, for example. One voxel is selected from space voxels(voxels having a type-information value of 0) at the time. If the parentvirtual sphere that has the diameter Ra and whose center is positionedat the selected voxel is placed and the parent virtual sphere overlapsthe matter voxel, another space voxel is selected again as the center.In this way, space voxels are selected one after another; and, if theparent virtual sphere at a voxel does not overlap the matter voxel, itis determined that the parent virtual sphere that has the diameter Racan be placed at the position. If the parent virtual spheres centered atall space voxels at the time overlap the matter voxel, it is determinedthat the parent virtual sphere that has the diameter Ra cannot beplaced. Note that the voxel serving as the center may be selected inrandom order; alternatively, the voxel may be selected in the order ofvoxels from the voxels on the inflow plane 61 to the voxels on theoutflow plane 62. The maximum value Ramax is equal to or more than themaximum diameter of normal pores in the porous partition 44 and can beset with reference to a value determined in an experiment, for example.If Step S230 determines that no parent virtual sphere can be placed, thediameter Ra is decremented by 1 (Step S240) and Step S230 and processessubsequent thereto are carried out. In this embodiment, the decrement isset to 1; however, the decrement can be appropriately set in accordancewith an acceptable calculation load or the like.

If Step S230 determines that a parent virtual sphere can be placed, thissingle parent virtual sphere having the diameter Ra is placed at theposition (Step S250). Specifically, in the porous-body table 81 of theporous-body data 80 stored in the RAM 24 in Step S200, the typeinformation of voxels occupied by the parent virtual sphere having thediameter Ra is changed to another value of 3, which indicates that thevoxels are occupied by the parent virtual sphere. In this embodiment,when the centers of voxels are contained within a parent virtual sphere,the type information of the voxels is changed to another value of 3.Alternatively, when a predetermined percentage (for example, 50%) ormore of the volume of voxels are occupied by a parent virtual sphere,the type information of the voxels may be changed to another value of 3;the type information of only the voxels completely contained within aparent virtual sphere may be changed to another value of 3; or when atleast portions of voxels are occupied by a parent virtual sphere, thetype information of the voxels may be changed to another value of 3.This is also the case for voxels occupied by child virtual spheresdescribed below.

Subsequently, the CPU 22 sets the diameter Rb of a child virtual sphereto the same value as that of the diameter Ra (Step S260) and determinesas to whether or not the child virtual sphere having the diameter Rb canbe placed within space voxels inside the virtual wall surfaces definedin Step S210 (Step S270). The child virtual sphere having the diameterRb is a virtual sphere that has a size with a diameter of Rb (μm), whosecenter is positioned at the center of one of voxels, and shares someoccupied voxels with the parent virtual sphere. The child virtual sphereis placed such that the center of the child virtual sphere overlaps theparent virtual sphere that has been placed in Step S250. Whether or notthe child virtual sphere having the diameter Rb can be placed isdetermined in the following manner, for example. One voxel is selectedfrom voxels occupied by the parent virtual sphere (voxels having atype-information value of 3) at the time. If the child virtual spherethat has the diameter Rb and whose center is positioned at the selectedvoxel is placed and the child virtual sphere overlaps the matter voxel,another voxel occupied by the parent virtual sphere is selected as thecenter. In this way, the voxels are selected one after another; and, ifthe child virtual sphere at a voxel does not overlap the matter voxel,it is determined that the child virtual sphere that has the diameter Rbcan be placed at the position. If the child virtual spheres centered atall space voxels occupied by the parent virtual sphere at the timeoverlap the matter voxel, it is determined that the child virtual spherethat has the diameter Rb cannot be placed.

If Step S270 determines that a child virtual sphere can be placed, thissingle child virtual sphere having the diameter Rb is placed at theposition (Step S280). Specifically, in the porous-body table 81 of theporous-body data 80 stored in the RAM 24 in Step S200, the typeinformation of voxels occupied by the child virtual sphere having thediameter Rb is changed to another value of 4, which indicates that thevoxels are occupied by the child virtual sphere. Note that this changein type information is not carried out for voxels having atype-information value of 3, which are occupied by the parent virtualsphere. In other words, the voxels that are occupied by both the parentvirtual sphere and the child virtual sphere are tagged with the typeinformation of the parent virtual sphere. After the single child virtualsphere is placed, Step S270 and processes subsequent thereto are carriedout and Step S280 is repeated to place child virtual spheres having thediameter Rb until it is determined that another child virtual spherehaving the diameter Rb can be no longer placed. Note that child virtualspheres are allowed to overlap each other. In other words, voxelsoccupied by a child virtual sphere are allowed to overlap voxelsoccupied by another child virtual sphere.

If Step S270 determines that no child virtual sphere can be placed, thediameter Rb is decremented by 1 (Step S290); it is determined as towhether or not the diameter Rb is less than a minimum value Rbmin (StepS300); if the diameter Rb is equal to or more than the minimum valueRbmin, Step S270 and processes subsequent thereto are carried out. Theminimum value Rbmin is the lower limit of the diameter Rb of childvirtual spheres. The minimum value Rbmin is a threshold that is definedso as not to place child virtual spheres that have a relatively smalldiameter and do not considerably influence the analysis result, forexample. In this embodiment, Rbmin is set to 2 μm.

If Step S300 determines that the diameter Rb is less than the minimumvalue Rbmin, a virtual curved surface solid is placed (Step S310), thevirtual curved surface solid being made up of the parent virtual spherethat has been placed in Step S250 and the child virtual spheres thathave been placed in Step S280. Specifically, in the porous-body table 81of the porous-body data 80 stored in the RAM 24 in Step S200, the typeinformation of voxels occupied by the parent virtual sphere (voxelshaving a type-information value of 3) and voxels occupied by the childvirtual spheres (voxels having a type-information value of 4) is changedto another value of 5, which indicates that the voxels are curvedsurface solid voxels occupied by the virtual curved surface solid. Inaddition, the positional information of the curved surface solid voxelswhose type information has been changed to another value of 5 this timeis associated with the identification code of the virtual curved surfacesolid. Such identification codes of virtual curved surface solids arevalues individually allocated in the order that the virtual curvedsurface solids are placed, for example. The curved surface solid voxelsof a single virtual curved surface solid are associated with the sameidentification code. The information regarding the virtual curvedsurface solid is stored in the RAM 24 (Step S320) and it is determinedas to whether or not 99% or more of space voxels are substituted withthe curved surface solid voxels (Step S330). Specifically, withreference to the type information of voxels in the porous-body table 81stored in the RAM 24, this determination is carried out as to whether ornot the ratio of the number of voxels having a type-information value of5 to the total number of the voxels having a type-information value of 0and the voxels having a type-information value of 5 is 99% or more. Notethat the threshold used in this determination is not limited to 99% andanother value may be employed. If the ratio of space voxels that havebeen substituted with curved surface solid voxels is less than 99% inStep S330, Step S230 and processes subsequent thereto are carried out toplace another virtual curved surface solid. If the ratio of space voxelsthat have been substituted with curved surface solid voxels is 99% ormore in Step S330, the virtual-curved surface-solid placement process isfinished.

Note that, during the placement of virtual curved surface solids oneafter another by repeating Step S230 and processes subsequent thereto,in this embodiment, voxels occupied by an virtual curved surface solidplaced at a time are allowed to overlap voxels occupied by anothervirtual curved surface solid that has been placed. Specifically, in StepS230 in the virtual-curved-surface-solid placement process, even when aparent virtual sphere having a diameter Ra to be placed overlaps avirtual curved surface solid that has been placed, this parent virtualsphere is allowed to be placed. In other words, in Step S230, if aparent virtual sphere having a diameter Ra does not overlap the mattervoxel, regardless of whether or not the parent virtual sphere overlapsvirtual curved surface solids that have been placed, Step S230determines that the parent virtual sphere having a diameter Ra can beplaced at the position. Similarly, in Step S270, even when a childvirtual sphere having a diameter Rb to be placed overlaps a virtualcurved surface solid that has been placed, this child virtual sphere isallowed to be placed. In other words, in Step S270, if a child virtualsphere having a diameter Rb does not overlap the matter voxel,regardless of whether or not the child virtual sphere overlaps virtualcurved surface solids that have been placed, Step S270 determines thatthe child virtual sphere having a diameter Rb can be placed at theposition. As a result, compared with the cases where virtual curvedsurface solids are placed so as not to overlap other virtual curvedsurface solids, virtual curved surface solids having a relatively largevolume can be placed.

In Step S320, the virtual-curved-surface-solid table 83 serving asinformation regarding virtual curved surface solids is stored as a partof the porous-body data 80 in the RAM 24. Thevirtual-curved-surface-solid table 83 includes association among theidentification code of each virtual curved surface solid, the centralcoordinates (X, Y, Z) and diameter of the parent virtual sphere of thevirtual curved surface solid, and the central coordinates and diameterof at least one child virtual sphere of the virtual curved surfacesolid. FIG. 8 describes an example of the virtual-curved-surface-solidtable 83. As described in this drawing, the virtual-curved-surface-solidtable 83 includes, regarding each of a plurality of virtual curvedsurface solids that have been placed as a result of repeating of StepsS230 to S320, association among the identification code, the centralcoordinates and diameter of the parent virtual sphere, and the centralcoordinates and diameter of at least one child virtual sphere of thevirtual curved surface solid. Since some virtual curved surface solidseach include a plurality of child virtual spheres, such an virtualcurved surface solid is associated with information of the plurality ofchild virtual spheres: the child virtual spheres can be identified asthe first child virtual sphere, the second child virtual sphere, . . . ,in the order that these spheres are placed, for example. Note that avirtual curved surface solid that has no child virtual sphere, that is,an virtual curved surface solid made up of a parent virtual spherealone, may be placed.

As a result of the virtual-curved-surface-solid placement process, thevirtual-curved-surface-solid table 83 is stored in the RAM 24 and theplacement of virtual curved surface solid results in substitution ofspace voxels with curved surface solid voxels. Hereinafter, the mannerin which the virtual-curved-surface-solid placement process is carriedout to place a single virtual curved surface solid made up of a parentvirtual sphere and child virtual spheres will be described. FIGS. 9A and9B illustrate explanatory views of placement of a parent virtual sphere.FIGS. 10A and 10B illustrate explanatory views of placement of childvirtual spheres and a virtual curved surface solid. For convenience ofexplanation, FIGS. 9A, 9B, 10A and 10B illustrate sections parallel tothe X direction in the porous-body data 80 and two-dimensionallyillustrate the placement of the virtual curved surface solid. FIG. 9A isan explanatory view of an example of the porous-body data 80 in whichStep S210 has just been carried out and a virtual curved surface solidis to be placed. FIG. 9B is an explanatory view in which a single parentvirtual sphere is placed. FIG. 10A is an explanatory view in which aplurality of child virtual spheres are placed for the parent virtualsphere that has been placed in FIG. 9B. FIG. 10B is an explanatory viewin which a virtual curved surface solid made up of the parent virtualsphere and child virtual spheres is placed. As illustrated in FIG. 9A,the porous-body data 80 is made up of matter voxels and space voxels;and, the inflow plane 61, the outflow plane 62, and the virtual wallsurfaces 85 are defined. The virtual curved surface solid (parentvirtual sphere and child virtual spheres) is placed so as not to extendbeyond the virtual wall surfaces 85. In this state, the processes ofSteps S220 to S250 are carried out: in a case where the diameter Ramaxis set to a sufficiently large value, the diameter Ra is decremented by1 in a stepwise manner; and when the diameter Ra is decremented to beequal to the maximum diameter of a parent virtual sphere that can beplaced in the porous-body data 80 so as not to overlap the matter voxeland so as not to extend beyond the virtual wall surfaces 85, this singleparent virtual sphere is placed (FIG. 9B). Subsequently, Steps S270 toS300 are repeated until Step S300 determines that the diameter Rbbecomes less than the minimum value Rbmin. As a result, a plurality ofchild virtual spheres having various diameters are placed such that thecenters of the child virtual spheres overlap the parent virtual sphere,and the voxels occupied by the child virtual spheres do not overlap thematter voxel and fill space voxels (FIG. 10A). After Step S300determines that the diameter Rb is less than the minimum value Rbmin, asingle virtual curved surface solid made up of the parent virtual sphereand the child virtual spheres that have been placed is placed (FIG.10B). In this way, processes of Steps S230 to S320 in which a singlevirtual curved surface solid is placed are repeated until Step S330determines that 99% or more of space voxels have been substituted withthe curved surface solid voxels. Thus, virtual curved surface solids areplaced one after another in other space voxels in which virtual curvedsurface solids have not been placed yet, to thereby fill space voxelswith curved surface solid voxels. As a result, spaces (pores) havingcomplex shapes in a porous body are substituted with virtual curvedsurface solids each made up of a combination of a plurality of spheres,so that the spaces within the porous body can be simulated with higheraccuracy as a combination of a plurality of virtual curved surfacesolids.

Hereinafter, the description of the analysis processing routine in FIG.6 will be resumed. After the virtual-curved-surface-solid placementprocess of Step S100 is finished, the CPU 22 carries out a fluidanalysis process (Step S110) in which fluid analysis is carried out onthe basis of the porous-body data 80 stored in the RAM 24 to therebyobtain information regarding flow rates in individual space voxelsduring passing of a fluid through the porous body. This fluid analysisprocess is carried out by the well-known lattice Boltzmann method.Specifically, the fluid analysis is carried out by the lattice Boltzmannmethod in the following manner: the central points of voxels of theporous-body data 80 are defined as lattice points; a predeterminedrelational expression regarding flows of a fluid entering through theinflow plane 61 and flowing between each lattice point and its adjacentlattice point is used. As information regarding the flow rates inindividual space voxels, flow-rate vectors each made up of flow rate andflow direction in individual space voxels of the porous-body data 80 areobtained. The flow-rate vectors in individual space voxels areassociated with the porous-body table 81 of the porous-body data 80 inthe RAM 24 and stored. Note that this fluid analysis is carried out withnumerical values that are necessary for the analysis and are defined inadvance in, for example, the HDD 25 or the like, such as a fluid averageflow rate T_(in) at the inflow plane 61, a fluid viscosity μ, and afluid density ρ. These numerical values may be set by the user via theinput devices 27. The average flow rate T_(in) is the average flow rateof the fluid immediately before entry into the porous body andcorresponds to the initial value of the flow rate in the fluid analysis.In this embodiment, the average flow rate T_(in) is set to 0.01 m/s. Thefluid is assumed to be the air at 0° C. and at 1 atm having a viscosityμ of 1.73×10⁻⁵ [Pa·s] and a density ρ of 1.25 [kg/m³]. Note that thefluid analysis process in Step S110 is carried out such that the virtualcurved surface solids that have been placed in Step S100 are notconsidered and the curved surface solid voxels are also assumed to bespace voxels. In this embodiment, the fluid analysis process in StepS110 is carried out on the basis of the porous-body data 80 stored inthe RAM 24. Alternatively, the fluid analysis process in Step S110 maybe carried out on the basis of the porous-body data 60 stored in the HDD25.

Subsequently, the CPU 22 carries out a flow-rate-weighted mean diameterevaluation process (Step S120) of obtaining the flow-rate-weighted meandiameter Ru and determining the quality of the porous body on the basisof this obtained value to thereby evaluate the trapping capability ofthe porous body. This process is carried out with information regardingthe plurality of virtual curved surface solids that have been placed inStep S100 and information regarding the flow rates that have beenobtained by the fluid analysis in Step S110. The flow-rate-weighted meandiameter Ru is obtained by an expression (1) below.

$\begin{matrix}{\left\lbrack {{Math}.\mspace{14mu} 1} \right\rbrack \mspace{641mu}} & \; \\{{Ru} = \frac{\sum\limits_{i = 1}^{n}\left( {R_{i}^{\prime} \times V_{i} \times U_{i}} \right)}{\sum\limits_{i = 1}^{n}\left( {V_{i} \times U_{i}} \right)}} & (1)\end{matrix}$

where

Ru: flow-rate-weighted mean diameter [μm]

n: number of virtual curved surface solids that have been placed[number]

R′_(i): equivalent diameter of each virtual curved surface solid [μm](i=1, 2, . . . , n)

V_(i): volume of each virtual curved surface solid [cc] (i=1, 2, . . . ,n)

U_(i): average flow rate of fluid passing through each virtual curvedsurface solid [mm/s] (i=1, 2, . . . , n).

In this expression, the number n of the virtual curved surface solidsthat have been placed is equal to the total number of virtual curvedsurface solids that have been placed in the virtual-curved-surface-solidplacement process of Step S100. The equivalent diameter R′_(i), volumeV_(i), and average flow rate U_(i) of each virtual curved surface solidare obtained in the following manner, for example. A single virtualcurved surface solid is selected and curved surface solid voxelscorresponding to the identification code of the selected virtual curvedsurface solid are examined with reference to the porous-body table 81 inthe RAM 24. The number of voxels of curved surface solid voxels of theselected virtual curved surface solid is obtained; and the product ofthe number of voxels and the volume of a single curved surface solidvoxel (in this embodiment, 1.728 μm³) is defined as the volume V_(i). Inaddition, on the basis of information (the central coordinates anddiameters of the parent virtual sphere and child virtual spheres)contained in the virtual-curved-surface-solid table 83, the surface areaS_(i) of the selected virtual curved surface solid is obtained. Theequivalent diameter R′_(i) is obtained by equivalent diameterR′_(i)=6×(volume V_(i) of virtual curved surface solid)/(surface areaS_(i) of virtual curved surface solid). In addition, the quantity Q_(i)of the fluid passing through the selected virtual curved surface solidper unit time is obtained; and the average flow rate U_(i) is obtainedby average flow rate U_(i)=Q_(i)/{π(R′_(i))²/4}.

In this embodiment, the voxels occupied by different virtual curvedsurface solids are allowed to overlap. For this reason, the volume V_(i)used in the expression (1) is a value modified such that voxels eachoccupied by a plurality of virtual curved surface solids (that is,curved surface solid voxels each serving as components of a plurality ofvirtual curved surface solids) are each assumed to be occupied only byany one of the virtual curved surface solids. Specifically, the volumeV_(i) is modified by assuming that curved surface solid voxels eachserving as components of a plurality of virtual curved surface solidsare each a component that belongs only to a single virtual curvedsurface solid having the largest equivalent diameter R′_(i) among theplurality of virtual curved surface solids; and the modified value isused in the expression (1). This is carried out in the following manner,for example. Without consideration as to whether or not the curvedsurface solid voxels each serve as components of plurality of virtualcurved surface solids (that is, the curved surface solid voxels are eachassumed to serve as components of any corresponding virtual curvedsurface solids), the volume V_(i) is obtained. Thus, the volume V_(i)before modification is obtained. On the basis of the volume V_(i) beforemodification, the equivalent diameter R′_(i) is obtained. The volumeV_(i) of virtual curved surface solids is obtained again in descendingorder of the equivalent diameter R′_(i). At this time, curved surfacesolid voxels that have been used once for obtaining volume V_(i) are nolonger used for calculation of the volume V_(i) of other virtual curvedsurface solids (these curved surface solid voxels are no longer countedfor obtaining the number of voxels of the curved surface solid voxels ofthe virtual curved surface solids). As a result, the volume V_(i)(modified volume V_(i)) can be obtained such that the curved surfacesolid voxels each serving as components of a plurality of virtual curvedsurface solids are each assumed to be a component that belongs only tothe virtual curved surface solid having the largest equivalent diameterR′_(i). This modified volume V_(i) is used as the volume V_(i) in theexpression (1). Note that the equivalent diameter R′_(i) used is a valuebased on the volume V_(i) before modification; and the modified volumeV_(i) is not used to obtain again the equivalent diameter R′_(i).

The quantity Q_(i) of the passing fluid is obtained in the followingmanner, for example. Among curved surface solid voxels of the selectedvirtual curved surface solid, the curved surface solid voxels formingthe surface of the virtual curved surface solid are identified on thebasis of information contained in the virtual-curved-surface-solid table83. The curved surface solid voxels forming the surface of the virtualcurved surface solid can also be identified by, for example,identifying, among curved surface solid voxels of the selected virtualcurved surface solid, curved surface solid voxels adjacent to any one ofspace voxels, matter voxels, and curved surface solid voxels of theother virtual curved surface solids. Alternatively, the curved surfacesolid voxels forming the surface of the virtual curved surface solid maybe identified on the basis of the central coordinates and diameters ofthe parent virtual sphere and child virtual spheres contained in thevirtual-curved surface solid table 83. Subsequently, flow-rate vectorsassociated with curved surface solid voxels forming the surface areexamined with the porous-body table 81 in the RAM 24 to identify curvedsurface solid voxels having flow-rate vectors pointing directions towardinside the virtual curved surface solid; and the magnitude of theflow-rate vectors of the identified curved surface solid voxels isobtained for each curved surface solid voxel. The quantity Q_(i) of thepassing fluid is obtained as quantity Q_(i) of the fluid passing perunit time=(sum of magnitude of flow-rate vectors)×(number of curvedsurface solid voxels having flow-rate vectors pointing directions towardinside virtual curved surface solid among curved surface solid voxelsforming surface of virtual curved surface solid)×(area (=1.44 μm²) ofsingle surface of curved surface solid voxel).

As described above, the CPU 22 provides the equivalent diameter R′_(i),volume V_(i), and average flow rate U_(i) of individual n virtual curvedsurface solids and provides the flow-rate-weighted mean diameter Ru byuse of the expression (1). In cases where the flow-rate-weighted meandiameter Ru obtained is 10 μm or more and 24 μm or less, the CPU 22evaluates that the porous body (region 50 in the porous partition 44)from which the porous-body data 60 is derived is good in terms oftrapping capability; and, in the other cases, the CPU 22 evaluates thatthe porous body is poor in terms of trapping capability. The CPU 22stores, in the RAM 24, for example, the value of the flow-rate-weightedmean diameter Ru and the evaluation result.

Subsequently, the CPU 22 carries out a difference ΔR evaluation process(Step S130) of providing a difference ΔR that is an absolute value ofthe difference between an arithmetic mean diameter Rc and theflow-rate-weighted mean diameter Ru and determining the quality of theporous body on the basis of the provided value to thereby evaluate thetrapping capability of the porous body. This process is carried out withinformation regarding the plurality of virtual curved surface solidsthat have been placed in Step S100 and the flow-rate-weighted meandiameter Ru that has been obtained in Step S120. The difference ΔR isobtained in the following manner. The arithmetic mean diameterRc=(R′₁+R′₂+ . . . +R′_(n))/n is obtained. The arithmetic mean diameterRc may be obtained through the calculation of equivalent diameter R′_(i)as in Step S120 or may be obtained with the values of equivalentdiameter R′_(i) that have been obtained in Step S120. Then, thedifference ΔR is obtained by the difference ΔR=|Ru−Rc|. In cases wherethe CPU 22 evaluates the porous body as being good in theflow-rate-weighted mean diameter evaluation process in Step S120 and thedifference ΔR obtained is 2 μm or less, the CPU 22 evaluates that theporous body (region 50 in the porous partition 44) from which theporous-body data 60 is derived is better in terms of trappingcapability; and, in the other cases, the CPU 22 evaluates that theporous body is not “better”. In other words, in this embodiment, incases where the porous body is evaluated as being good in Step S120 (theflow-rate-weighted mean diameter Ru is 10 μm or more and 24 μm or less)and the porous body is evaluated as being good in Step S130 (thedifference ΔR is 2 μm or less), the porous body is evaluated as being“better” in terms of trapping capability. In cases where the evaluationresult is good in Step S120 but the evaluation result is not good inStep S130, the porous body is evaluated as being “good” in terms oftrapping capability. In cases where the evaluation result is poor inStep S120, regardless of the evaluation result in Step S130, the porousbody is evaluated as being “poor” in terms of trapping capability. TheCPU 22 stores, in the RAM 24, the values of the arithmetic mean diameterRc and difference ΔR and the evaluation results.

After carrying out the evaluation processes of Steps S120 to S130, theCPU 22 carries out an analysis-result output process (Step S140) ofoutputting analysis result data such as information stored in the RAM 24during the processes and storing the analysis result data in the HDD 25,and finishes the routine. The analysis result data includes, forexample, those stored in the RAM 24, such as the porous-body data 80including the porous-body table 81, the inflow-outflow table 82, and thevirtual-curved-surface-solid table 83; the value of theflow-rate-weighted mean diameter Ru and the evaluation result obtainedin Step S120; and the values of the arithmetic mean diameter Rc anddifference ΔR and the evaluation results obtained in Step S130. Theanalysis result data may also include values used in processes of StepsS120 to S130, such as the equivalent diameter R′_(i), the volume V_(i),and the average flow rate U_(i); and values used in the fluid analysisprocess in Step S110, such as the average flow rate T_(in), the fluidviscosity μ, and the fluid density ρ.

The porous partition 44 of this embodiment is subjected to theabove-described analysis of the microstructure and, as a result of theanalysis, it is found to have a flow-rate-weighted mean diameter Ru of10 μm or more and 24 μm or less. It is more preferable that thedifference ΔR is 2 μm or less.

Hereinafter, a method for producing the honeycomb filter 30 includingthe porous partitions 44 according to this embodiment will be described.Here, a method for producing the honeycomb filter 30 including theporous partitions 44 mainly composed of cordierite will be described asan example.

The porous partitions 44 of the honeycomb filter 30 can be produced by araw-material mixing step of mixing a base material and a pore-formingagent, to provide green body; and a molding and firing step of moldingthe green body to provide a compact and firing this compact. The basematerial is a mixture of talc having an average particle size of 1 μm ormore and 18 μm or less, alumina, and an auxiliary raw materialcontaining a material that undergoes a eutectic reaction with talc andbeing prepared in an amount so as to satisfy a weight ratio of 0.5% ormore and 1.5% or less by weight relative to the talc. The talcpreferably has an average particle size of 5 μm or more and 12 μm orless. The weight ratio of the alumina to the talc is 30% or more and 45%or less by weight, for example. The base material may further containsilica in an amount so as to satisfy a weight ratio of 42% or more and56% or less by weight relative to the talc, or magnesia in an amount soas to satisfy a weight ratio of 12% or more and 16% or less by weightrelative to the talc. The auxiliary raw material is at least oneselected from zirconium oxide, cerium oxide, and yttrium oxide, forexample. The weight ratio of the auxiliary raw material relative to thetalc is more preferably 0.5% or more and 1.0% or less by weight. Thepore-forming agent is preferably burnt off by firing to be carried out:starch, coke, or porous resin, for example. The raw-material mixing stepmay be carried out by adding, for example, a binder such asmethylcellulose or hydroxypropoxylmethylcellulose, water, and adispersing agent. The dispersing agent may be a surfactant such asethylene glycol. The process of preparing green body is not particularlylimited and may be carried out by a method using a kneader or a vacuumclay kneader, for example. The green body is, for example, extrudedthrough a die having a shape corresponding to the arrangement of thecells 34, so as to have the shape illustrated in FIGS. 1 and 2. In theextruded material, the cells 34 are sealed with the outlet sealingmaterial 38 and the inlet sealing material 42. Subsequently, theextruded material is subjected to a drying treatment, a calcinationtreatment, and a firing treatment to thereby produce the honeycombfilter 30 including the porous partitions 44. The outlet sealingmaterial 38 and the inlet sealing material 42 may be formed of the rawmaterial forming the porous partitions 44. The calcination treatment iscarried out at a temperature lower than the firing temperature, to burnoff organic components contained in the honeycomb filter 30. The firingtemperature is 1350° C. to 1440° C. and is preferably 1410° C. to 1430°C. By carrying out the above-described steps, the honeycomb filter 30including the porous partitions 44 can be obtained.

According to the embodiment having been described in detail so far, theporous partitions 44 formed of a porous body are found to have aflow-rate-weighted mean diameter Ru of 10 μm or more and 24 μm or lessas a result of the microstructure analysis using the user PC 20; andhence the porous partitions 44 have a sufficiently high trappingcapability. In addition, in cases where the difference ΔR is 2 μm orless, the porous partitions 44 have a higher trapping capability.

The larger the extent of variation in the volume V_(i) or average flowrate U_(i) among a plurality of virtual curved surface solids that havebeen placed, the larger the tendency for the flow-rate-weighted meandiameter Ru to become excessively large or small. Regarding pores of aporous body that are simulated with virtual curved surface solids havinga large volume V_(i), the probability that a fluid passing through thepores comes into contact with the wall surfaces of the porous body tendsto decrease. Regarding pores of a porous body that are simulated withvirtual curved surface solids having a small volume V_(i), a fluid tendsnot to pass through the pores or a catalyst tends not to beappropriately applied to the wall surfaces of the pores, the catalystbeing used for the porous body to be used as a filter. Regarding poresof a porous body that are simulated with virtual curved surface solidshaving an average flow rate U_(i) higher than the average flow rate(simple average flow rate) of the whole pores of the porous body, afluid passes through these pores in a short time and hence these porestend not to contribute to the trapping capability. Regarding pores of aporous body that are simulated with virtual curved surface solids havingan average flow rate U_(i) lower than the average flow rate (simpleaverage flow rate) of the whole pores of the porous body, the amount ofa fluid entering these pores is small and hence these pores tend not tocontribute to the trapping capability. As has been described, pores of aporous body that are simulated with virtual curved surface solids havingan excessively large or small volume V_(i) or an excessively high or lowaverage flow rate U_(i) tend not to contribute to the trappingcapability. This is probably the reason why, in porous bodies having alarge portion that tends not to contribute to the trapping capability,the flow-rate-weighted mean diameter Ru is found to be excessively largeor small; and the trapping capability probably correlates with theflow-rate-weighted mean diameter Ru. In cases where theflow-rate-weighted mean diameter Ru is 10 μm or more and 24 μm or less,the flow-rate-weighted mean diameter Ru is not excessively large orsmall and a sufficiently high trapping capability is probably achieved.Among cases where the flow-rate-weighted mean diameter Ru issubstantially the same, cases where the absolute value of the differencebetween the arithmetic mean diameter Rc and the flow-rate-weighted meandiameter Ru is small tend to achieve a better trapping capability of theporous body. Accordingly, a porous body that has a flow-rate-weightedmean diameter Ru of 10 μm or more and 24 μm or less and a difference ΔRof 2 μm or less tends to have a higher trapping capability.

In the production of the porous partitions 44, use of talc having anaverage particle size of 18 μm or less probably results in suppressionof generation of excessively large pores. By adding an auxiliary rawmaterial containing a material that undergoes a eutectic reaction withtalc, excessively small pores through which a fluid tends not to passare probably filled. In addition, the firing temperature of 1350° C. to1440° C. probably results in a sufficiently high strength of the porousbody. As a result, generation of excessively large or small pores issuppressed and generation of pores causing an excessively high or lowflow rate is suppressed; and this probably results in a high trappingcapability.

The present invention is not limited to the above-described embodiment.It is clear that the present invention can be implemented in a varietyof embodiments without departing from the technical scope thereof.

EXAMPLES

Hereinafter, an example in which a porous body according to the presentinvention was actually produced will be described as an Example. Notethat Experimental examples 1 to 3 are Comparative examples with respectto the present invention and Experimental example 4 is an Example of thepresent invention. However, the present invention is not limited to theExample described below.

Experimental Example 1

A honeycomb filter of Experimental example 1 was produced in thefollowing manner. A talc powder A having an average particle size of 12μm, alumina, and zirconium oxide (ZrO₂) serving as an auxiliary rawmaterial were prepared and mixed together to provide a base material.The weight ratio of the zirconium oxide (ZrO₂) to the talc powder A wasset to 1.75%. The weight ratio of the alumina to the talc powder A wasset to 201. The thus-obtained base material and a pore-forming agent(starch) having an average particle size of 30 μm were mixed together ina mass ratio of 100:30. This mixture was mixed with methylcelluloseserving as an organic binder and an appropriate amount of water tothereby provide green body. Subsequently, this green body was extrudedthrough a predetermined die to thereby provide a compact including theporous partitions 44 having the shape illustrated in FIGS. 1 and 2 (notethat the exterior of the compact had a shape of a quadrangular prism).Subsequently, the compact obtained was dried with microwaves, furtherdried with hot gas, then subjected to sealing of cell openings, calcinedin an oxidizing atmosphere at 550° C. for 3 hours, and then fired in aninert atmosphere at 1430° C. for 2 hours. The sealed portions wereformed in the following manner: masks were placed on alternate cellopenings at an end of the compact; and this masked end was immersed in asealing slurry (formed of the same material as the green body), so thatopenings and sealed portions were arranged alternately. Similarly, theother end was also masked and sealed portions were formed such thatcells having one open end and the other sealed end and cells having onesealed end and the other open end were alternately arranged. The compacthaving been fired was ground so as to have a cylindrical shape.Subsequently, the periphery of this cylinder was coated with a peripherycoating slurry prepared by kneading alumina silicate fibers, colloidalsilica, polyvinyl alcohol, SiC, and water. This slurry was cured bydrying to thereby form a peripheral protective part 32. Thus, thehoneycomb filter of Experimental example 1 was obtained. This honeycombfilter had a diameter of 118.4 mm in cross section, a length of 127 mm,a cell density of 360 cells/square inch, and a partition thickness of 5mil.

Experimental Example 2

A honeycomb filter of Experimental example 2 was produced as inExperimental example 1 except that the talc powder A was replaced by atalc powder B having an average particle size of 25 μm.

Experimental Example 3

A honeycomb filter of Experimental example 3 was produced as inExperimental example 1 except that the talc powder A was replaced by atalc powder C having an average particle size of 20 μm, the weight ratioof the zirconium oxide (ZrO₂) to the talc powder C was set to 1%, andthe firing temperature was set to 1420° C.

Experimental Example 4

A honeycomb filter of Experimental example 4 was produced as inExperimental example 1 except that the weight ratio of the zirconiumoxide (ZrO₂) to the talc powder A was set to 1% and the firingtemperature was set to 1420° C.

[Preparation of Microstructure Analyzer]

A microstructure analyzer for evaluating Experimental examples 1 to 4was prepared. An analysis processing program having the functiondescribed in the embodiment above was created. This program was storedin the HDD of a computer including a controller including a CPU, a ROM,and a RAM, and the HDD. Thus, the microstructure analyzer was prepared.

Analysis of Microstructure

The porous partitions (porous body) of the honeycomb filter ofExperimental example 1 were subjected to a CT scan. From the resultantvoxel data, a piece of data was extracted in which the length in the Xdirection was 300 μm (=1.2 μm×250 voxels), which was the same as thepartition thickness in the passing direction of exhaust gas, the lengthin the Y direction was 480 μm (=1.2 μm×400 voxels), and the length inthe Z direction was 480 μm (=1.2 μm×400 voxels). This data was definedas the above-described porous-body data 60 and stored in the HDD inExperimental example 1. The above-described analysis processing routinewas executed for the porous-body data 60 in Experimental example 1. Thisprovided analysis result data including, as described above, theporous-body table, the virtual-curved surface solid table, values of theflow-rate-weighted mean diameter Ru and difference ΔR, and values of theequivalent diameter R′_(i), volume V_(i), and average flow rate U_(i) ofeach virtual curved surface solid. Similarly, analysis result data wasobtained for Experimental examples 2 to 4. As a result, theflow-rate-weighted mean diameters Ru in Experimental examples 1 to 4were respectively 26.3 μm, 29.9 μm, 24.5 μm, and 23.7 μm. Thedifferences ΔR in Experimental examples 1 to 4 were respectively 2.0 μm,3.0 μm, 2.1 μm, and 2.1 μm.

[Measurement of Number of Leaked Particles]

Regarding Experimental examples 1 to 4, the number of leaked particleswas measured as a value representing the actual trapping capability.Specifically, the filters of Experimental examples 1 to 4 were attachedto the exhaust pipe of a car through which exhaust gas passes. Thegasoline engine of the car was run on the basis of NEDC (New EuropeanDriving Cycle)-mode driving to thereby pass a fluid containingparticulate matter (engine exhaust gas) through the filters. In thefluid having passed through the filters, the amount of remainingparticulate matter was measured as the number of leaked particles. Thisnumber of leaked particles was converted with respect to 1 km of drivingdistance. Thus, the number of leaked particles [number/km] was obtainedas a value representing the trapping capability.

Table 1 summarizes the average particle size of talc powders, the weightratio of the auxiliary raw material (zirconium oxide) to talc, thefiring temperature, the flow-rate-weighted mean diameter Ru, thedifference ΔR, and the number of leaked particles in Experimentalexamples 1 to 4. FIG. 11 is a graph illustrating the relationshipbetween the flow-rate-weighted mean diameter Ru and the number of leakedparticles in Experimental examples 1 to 4.

TABLE 1 Weight ratio of Flow-rate- Number of Particle size auxiliary rawFiring weighted mean Difference leaked of talc powder material to talctemperature diameter Ru ΔR particles [μm] (% by weight) [° C.] [μm] [μm][Number/s] Experimental 12 1.75% 1430° C. 26.3 2.0 8.67E+11 Example 1Experimental 25 1.75% 1430° C. 29.9 3.0 1.23E+12 Example 2 Experimental20   1% 1410° C. 24.5 2.1 6.54E+11 Example 3 Experimental 12   1% 1410°C. 23.7 2.1 5.45E+11 Example 4

Table 1 and FIG. 11 indicate the following. Comparison amongExperimental examples 1 to 4 indicates that the smaller theflow-rate-weighted mean diameter Ru, the smaller the number of leakedparticles (the higher the trapping capability). In Experimental example4 in which the flow-rate-weighted mean diameter Ru is 24 μm or less, thenumber of leaked particles was smaller than that in Experimentalexamples 1 to 3. In Experimental example 4, the condition that thenumber of leaked particles is 6×10¹¹ or less [particles/km], which isthe limit for exhaust gas emitted from automobiles (Euro 6 (2017 andafter)), was satisfied. Thus, the trapping capability was sufficientlyhigh. Note that FIG. 11 illustrates both the limit of Euro 6 (2017 andafter) (number of leaked particles: 6×10¹¹ [particles/km]) and the limitof Euro 6 (before 2017) (number of leaked particles: 6×1012[particles/km]) (broken lines in FIG. 11).

The present application claims priority of Japanese Patent ApplicationNo. 2014-072362 filed on Mar. 31, 2014, the entire contents of which areincorporated herein by reference.

What is claimed is:
 1. A porous body having a flow-rate-weighted meandiameter Ru of 10 μm or more and 24 μm or less, wherein theflow-rate-weighted mean diameter Ru is obtained as follows: based on animage obtained by three-dimensionally scanning the porous body,porous-body data is created in which positional information indicatingposition of a voxel in the image is associated with voxel-typeinformation indicating whether the voxel is a space voxel representingspace or a matter voxel representing object; a process is carried out inwhich a single parent virtual sphere is placed in the porous-body dataso as to have as large a diameter as possible so that the parent virtualsphere fills the space voxels without overlapping the matter voxel, atleast one child virtual sphere whose center overlaps the parent virtualsphere that has been placed is placed such that voxels occupied by theat least one child virtual sphere do not overlap the matter voxel andfill space voxels, and a single virtual curved surface solid made up ofthe parent virtual sphere and the at least one child virtual sphere isplaced such that curved surface solid voxels, which are voxels occupiedby the virtual curved surface solid, fill space voxels; this process isrepeated to place a plurality of the virtual curved surface solids suchthat voxels occupied by different virtual curved surface solids do notoverlap each other; based on the porous-body data, fluid analysis iscarried out by the lattice Boltzmann method in terms of a fluid flowingthrough a predetermined inflow plane into the porous body, to obtainflow-rate vectors of the fluid in individual space voxels during passingof the fluid through the porous body; and based on information regardingthe virtual curved surface solids that have been placed and informationregarding the flow-rate vectors in individual space voxels, theflow-rate-weighted mean diameter Ru is obtained by an expression (1)below $\begin{matrix}{\left\lbrack {{Math}.\mspace{14mu} 1} \right\rbrack \mspace{641mu}} & \; \\{{Ru} = \frac{\sum\limits_{i = 1}^{n}\left( {R_{i}^{\prime} \times V_{i} \times U_{i}} \right)}{\sum\limits_{i = 1}^{n}\left( {V_{i} \times U_{i}} \right)}} & (1)\end{matrix}$ where Ru: flow-rate-weighted mean diameter [μm] n: numberof virtual curved surface solids that have been placed [number] R′_(i):equivalent diameter of each virtual curved surface solid [μm] (i=1, 2, .. . , n) V_(i): volume of each virtual curved surface solid [cc] (i=1,2, . . . , n) U_(i): average flow rate of fluid passing through eachvirtual curved surface solid [mm/s] (i=1, 2, . . . , n).
 2. The porousbody according to claim 1, wherein, based on the information regardingthe virtual curved surface solids that have been placed, an arithmeticmean diameter Rc=(R′₁+R′₂+ . . . +R′_(n))/n is obtained, and adifference ΔR (=|Ru−Rc|) is 2 μm or less.
 3. A honeycomb filtercomprising a partition that include the porous body according to claim 1and form a plurality of cells of which one end is open and the other endis sealed and serving as a fluid channel.
 4. A method for producing aporous body, comprising: a raw-material mixing step of mixing talchaving an average particle size of 1 μm or more and 18 μm or less,alumina, an auxiliary raw material containing a material that undergoesa eutectic reaction with talc and being prepared in an amount so as tosatisfy a weight ratio of 0.5% or more and 1.5% or less by weightrelative to the talc, and a pore-forming agent, to provide green body;and a molding and firing step of molding the green body to provide acompact and firing this compact at a firing temperature of 1350° C. to1440° C.
 5. The method for producing a porous body according to claim 4,wherein the talc has an average particle size of 5 μm or more and 12 μmor less.
 6. The method for producing a porous body according to claim 4,wherein the weight ratio of the auxiliary raw material relative to thetalc is 0.5% or more and 1.0% or less by weight.
 7. The method forproducing a porous body according to claim 4, wherein the auxiliary rawmaterial is at least one selected from zirconium oxide, cerium oxide,and yttrium oxide.
 8. The method for producing a porous body accordingto claim 4, wherein the firing temperature is 1410° C. to 1430° C.